Decimal to binary conversion is the process of converting a number from base-10 (decimal) to base-2 (binary). Each digit in a binary number represents a power of 2. To convert, you repeatedly divide the decimal number by 2, noting the remainders at each step. The binary equivalent is obtained by reading the remainders in reverse order.
For example, to convert the decimal number 13 to binary:
Reading the remainders in reverse order, we get 1101, so $13_{10} = 1101_2$.
Match the terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Decimal | A. Base-2 numeral system |
| 2. Binary | B. A digit in binary, either 0 or 1 |
| 3. Bit | C. The rightmost bit |
| 4. Least Significant Bit (LSB) | D. Base-10 numeral system |
| 5. Most Significant Bit (MSB) | E. The leftmost bit |
(Match the numbers 1-5 to the letters A-E)
Complete the following paragraph using the words provided: (powers, 2, remainders, base, binary)
Decimal to _______ conversion involves expressing a _______-10 number in _______-2. This is achieved by repeatedly dividing the decimal number by _______ and noting the _______. The _______ equivalent is read by taking the _______ in reverse order.
Explain in your own words why binary is used extensively in computer systems. What are its advantages?
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